Using Excel in RAMS courses at NTNU
By Jørn Vatn
Date 2014-07-05
1.
Comma, semicolon and VBA strings .................................................................................. 2
1.1 Decimal symbol ........................................................................................................... 2
1.2 List separator ............................................................................................................... 2
1.3 Syntax for VBA-strings ............................................................................................... 2
1.4 Editing the Region and Language ............................................................................... 2
2. Introduction problems ......................................................................................................... 3
3. Basic worksheet operations................................................................................................. 4
3.1 Using “variable names” in the excel sheet .................................................................. 4
3.2 Cell operations ............................................................................................................. 5
3.3 Plotting the results ....................................................................................................... 5
3.4 Using the Solver (Problemløser) Add-In to minimize the value of a cell ................... 6
3.5 What if analysis ........................................................................................................... 8
4. Creating and using VBA functions ..................................................................................... 9
4.1 Introduction ................................................................................................................. 9
4.2 Simple functions ........................................................................................................ 11
4.3 Advanced VBA functions .......................................................................................... 12
4.4 Built in functions ....................................................................................................... 13
4.5 Importing and exporting modules.............................................................................. 13
5. VBA Examples ................................................................................................................. 15
5.1 The effective failure rate in age related models ........................................................ 15
6. Monte Carlo Simulation .................................................................................................... 17
7. Feedback ........................................................................................................................... 18
8. Index ................................................................................................................................. 19
1.Comma, semicolon and VBA strings
MS Excel treats numbers and lists according to definitions given in "Region and Language".
Below we discuss the following
1. Decimal symbol
2. List separator
3. Syntax for VBA-strings
The discussion below relates to MS Excel. There might be different approaches in Excel for
the Mac.
1.1Decimal symbol
In many languages the comma (,) is the symbol used to separate the decimal part of a number
from the integer. For example we write π ≈ 3,14. In the English language a period (.) is used,
and one writes π ≈ 3.14. I this course a period is used as the decimal symbol in slides, course
compendium and in MS Excel demonstrations. It is recommended to edit the “Regional
settings” on your computer so that the period is used as the decimal symbol. This is explained
later down.
1.2List separator
Many functions in MS Excel require two or more arguments. For example to find the larges
value fo two A1 and A2 we may use the Max() function, by e.g., typing in cell A3:
=Max(A1,A2). Note that the English name of the maximum function is used. If your MS
Excel is set up with a national language, the Max() function has to be replaced by a national
language variant, e.g., Størst() in Norwegian. The separator between the two arguments is
here the comma (,), i.e., the list separator corresponding to a standard English configuration in
the Regional settings. In Norwegian and many other European countries the standard list
separator is the semi colon (;). It is recommended to edit the “Regional settings” on your
computer so that the comma is used as the list separator. This is explained later down.
1.3Syntax for VBA-strings
In the routine for numerical integration in pRisk.xls (supported in some NTNU courses), the
integrand is processed by visual (VBA). The integrand is enclosed in (") in pRisk.xls, and this
text string has to be stated in English syntax, i.e., if numbers are specified they have to have
the period as the decimal symbol, and when arguments are to be separated, the comma has to
be used as list separator. Not that this applies independent on your Regional setting.
1.4Editing the Region and Language
To change the standard configuration of your PC, choose the Control panel from the Start
button on the lower left corner of your screen. Then choose Region and Language. At the
bottom of this menu Additional settings.... From this menu you may edit the symbols used
for the decimal symbol and the list.
2.Introduction problems
Problem 1
We are considering the maintenance of an emergency shutdown valve (ESDV). The ESDV
has a hidden function, and it is considered appropriate to perform a functional test of the valve
at regular intervals of length . The cost of performing such a test is NOK 10 000. If the
ESDV is demanded in a critical situation, the total (accident) cost is NOK 10 000 000. The
rate of demands for the ESDV is one every 5 year. The failure rate of the ESDV is 210-6 (hrs1
). Determine the optimum value of  by:
 Finding an analytical solution
 Plotting the total cost as a function of 
 Minimising the cost function by means of numerical methods
Problem 2
In order to reduce testing it is proposed to install a redundant ESDV. The extra yearly cost of
such an ESDV is NOK 15 000. Determine the optimum test interval if we assume that the
second ESDV has the same failure rate, but that there is a common cause failure situation,
with  = 0.1. Will you recommend the installation of this redundant ESDV?
3.Basic worksheet operations
3.1Using “variable names” in the excel sheet
When using Excel from the worksheet windows, cells could be referred to by the row/column
name of the cell, e.g. A1 is the name of the upper left cell. The cell name is shown in the
Name Box pointed to by the arrow in Figure 1.
Figure 1 Name Box
If we want to refer to the value within this cell in an expression, we could just refer to the cell
by its name. For example, if we in cell B1 want to calculate the square of the value in A1, we
just type =A1^2 in cell B1.
When a lot of variables are defined in a worksheet, it will not be easy to read the formulas
used if we are always referring to variables by more or less arbitrary names. Hence, we would
like to give the variables more meaningful names. For example, if the cell A1 represents
temperature, we would rather refer to e.g. Temp, rather than A1. In order to accomplish this,
we just type Temp in the Name Box input filed. Now, the expression we would like to type in
cell B1 would be more easy to read, .e.g. we type =Temp^2.
Note, that if you want to use a variable like x2, it would be natural to write X2 in the cell
window. However, since X2 is a cell name already defined by Excel, this will not work (the
result would be that the active cell changes to X2). In order to prevent confusion with the
predefined cell names in Excel, we rather specify X_2.
Further note that we could specify more than one name for each cell. This will however be
difficult to trace, and should be avoided. If we by accident give one cell a wrong name, we
should first delete the cell name, before we give a new cell name. To delete the cell name,
choose Name Manager from the Formulas tab. Then search for the cell name to delete.
If we have given a cell on one worksheet a name, we could refer to this cell from an arbitrary
other work sheet just by specifying the cell name we have given. If we have not given a cell a
name, and want to refer to it from another worksheet we have to prefix the cell name with the
worksheet name, e.g. =Sheet1!A1.
Often we label the variables to use in one column, and then insert their values in the column
to the right. To easy give the corresponding cells the names given in the label cells then:
1.
2.
3.
4.
Give variable names in a column of cells.
Mark these cells and the column to the right.
On the Formulas tab, in the Defined names group, click Create from Selection
Tick Left column, and press OK in Figure 2.
.
Figure 2 Create cell names from selection
Ensure that the labels for the variables are legal cell names, i.e., do not contain blanks or
special symbols. If predefine cell names like A1 is used, Excel will add a “_” to the variable
name, e.g., A1_.
3.2Cell operations
To sum a range of cells and put the result in another cell, move the cell selector to the cell you
want to store the result in, and type =Sum(, then drag the cell selector over the cells you want
to sum, release the mouse button, and click Enter. Excel automatically completes the formula,
e.g. the resulting formula will be e.g. =SUM(A1:A5). Note that national versions of Excel
require national function names when used from the worksheets. Other functions that often
are used to manipulate cells would be =AVERAGE(A1:A5), =STDEV(A1:A5),
=MIN(A1:A5) and =MAX(A1:A5). For more advanced functions, we refer to the Excel
Help function.
3.3Plotting the results
Excel provides a wide range of possibilities for visualising the data stored in the worksheets.
Very often we have data where one column represent x-values, and subsequent columns
represent y-values. To draw graphs representing the various y-values:
1. Mark the corresponding cells (were the x-values are stored in the first column and the
y-values are stored in the second column)
2. On the Insert tab, in the Chart group, click Scatter
3. Select an appropriate chart sub-type.
Example
Consider Problem 1. The cost per time unit would be
C(tau) = PMCost/tau + tau*lambda*dRate*HCost
where we have specified the parameters like:
Parameter Value
PMCost
10000
Hcost
1E+07
lambda
0.01752
dRate
0.2
Figure 3 Parameters for Problem 1
Where the legend for each variable in Figure 3 corresponds to the cell name we have
specified. To plot the cost function, we specify the tau values in one column, then the PM
cost, the Accident (Risk) cost and the total cost in subsequent columns, e.g.
12 Tau
PM
Risk
Tot
13
0.4
25 000
7 008 32 008
14
0.5
20 000
8 760 28 760
15
0.6
16 667 10 512 27 179
Figure 4 Section of data to plot
In cell A13 we specify 0.4, then in cell A14 we write =A13+0.1. We may now copy the
formula in cell A14 by first selecting cell A14, pressing <Ctrl>C, then selecting the cell A14
to A34, and pressing <Ctrl>V. In cell B13 we specify =PMCost/A13. In column C13 we
specify =lambda*A13/2*Hcost*dRate. The total cost are now entered in cell D13 by
=B13+C13. Cells B13-D13 are then copied to subsequent rows. To find the minimum cost
graphically, we create the plot in Figure 5.
60 000
50 000
40 000
PM
30 000
Risk
Tot
20 000
10 000
0
0
0.5
1
1.5
2
2.5
Figure 5 Plot of data in problem 1
3.4Using the Solver (Problemløser) Add-In to minimize the value of a cell
In problem 2 we might calculate the total cost for a given inspection interval tau by a step of
calculations, see Figure 6.
Parameter Value
PMCost
10 000
Hcost
10 000 000
lambda
0.01752
dRate
0.2
beta
0.1
n
2
k
1
tau
0.7
PDFC
0.0006132
PDFI
4.061E-05
PFD
0.0006538
PM
14285.714
Accident
1307.6191
TotCost
15593.333
Formula
=beta*lambda*tau/2
=COMBIN(n,n-k+1)*((1-beta)*lambda*tau)^(n-k+1)/(n-k+2)
=PDFC+PDFI
=PMCost/tau
=PDF*dRate*HCost
=PM+Accident
Figure 6 Calculation of total cost in Problem 2
We now use the solver to minimize the total cost:
1. On the Data tab, in the Analysis group, click Solver1
.
2. In the Set Objective box, enter a cell reference or name for the objective cell. The
objective cell must contain a formula. In the example specify TotCost.
3. Do one of the following:
a. If we want the value of the objective cell to be as large as possible, click
Max.
b. If we want the value of the objective cell to be as small as possible, click
Min. Since we will like to minimize cost, click Min.
c. If we want the objective cell to be a certain value, click Value of, and
then type the value in the box.
4. In the By Changing Variable Cells box, enter a name or reference for each
decision variable cell range. Separate the nonadjacent references with commas. The
variable cells must be related directly or indirectly to the objective cell. In the
example, specify tau.
5. In the Subject to the Constraints box, enter any constraints that you want to apply.
See Excel Help for more instructions.
1
If the Solver command or the Analysis group is not available, you need to load the Solver Add-in
program (In Norwegian Solver = Problemløser).
1.
Click the File tab, click Options, and then click the Add-Ins category.
2.
In the Manage box, click Excel Add-ins, and then click Go.
3.
In the Add-ins available box, select the Solver Add-in check box, and then click OK.
3.5What if analysis
Another way to find this minimum would be to use so-called What-If analysis.
1. Create the tau-values in one column. This is accomplished similar to what was done
in Section 3.3
2. Lave the column to the right for Excel to fill in
3. In the cell just above the upper destination cell for the total cost values, specify
=TotCost.
4. Mark two columns, the first column represent the tau values, and the second column
represent the destination cells for the total cost. When marking these cells, also
include the row above the data cells, i.e. the row containing the =TotCost cell
5. On the Data tab, in the Data tools group, click What-If-Analysis
.
6. Select Data Table.
7. In the Column input cell, specify tau, see Figure 7.
Figure 7 Specification of Column input cell
Excel will now recalculate the total cost by changing the value of the tau cell according to the
list of tau values stored in the first column of the selected area. Then Excel store the result in
the second column of the selection.
4.Creating and using VBA functions
4.1Introduction
VBA is the programming language offered by Microsoft Office programs (Word, Excel etc).
The basic principles and syntax is similar for all VBA’s independent of which program they
are used in. However, the way we access data are quite different. In e.g. Excel data from the
worksheets are specified with the Range() function, whereas in Access stronger database
functions are available. Note also that Excel provides a very nice set of worksheet functions
that also are available from the VBA code. These functions are generally not available from
other Office programs, meaning that using these functions cause problems if you want to copy
the code to e.g. Access.
Note that Excel files containing VBA code need to be Saved As an Excel Macro-enabled
Workbook (*.xlsm).
To invoke the VBA editor, just press <Alt>F11. In the VBA editor, choose Insert and Module
to create a module for storing the function.
The different VBA functions and procedures are stored in so-called modules. The modules are
default given name by Excel, i.e. the first one starts with Module 1, the second Module 2 and
so on. It is however, possible to give the modules new names that are more informative, e.g.
NumIntLib for a library of procedures for numerical integration. It is a good idea to collect
procedures and functions that relates to each other in one module. A module comprises two
main parts:


Common declarations
The functions and procedures
In the declaration part you typically define variables that are common to all functions in one
module, or that should be common to all modules. In the declaration part we specify either
variables that should be available only from the actual module. These variables are specified
by the Private statement, e.g.
Private xValue As Single
Note that this statement should be given in the top of the module before any declaration of
functions or procedures. Later on, in a function or a procedure you may use the variable
xValue. Note that the xValue will be available in all procedures and functions in the module
where it is defined. This means that you might give a value to xValue in one function, and
then use this value in another function.
Sometimes you want variables to be available from all functions in all modules. You then use
the Public statement, e.g.
Public TimeUnit As String
You might in one module, e.g. the InitModule write a function that set the TimeUnit, e.g.
TimeUnit = ”Hours”
and you then access the value from another module, e.g.
MsgBox ”The time unit is ” & TimeUnit
Most variables you need should however, only be defined within one function. E.g. if you
need a counter, you define it within one function, e.g.
Function Sum1To10()
Dim x as integer
Dim s as single
X=0
For x = 1 To 10
s = s + x
Next x
Sum1To10 = s
End Function
Figure 8 Using the Dim statement
In Figure 8 we have used the Dim statement to define the variables x and s. Note that x and s
would not be available form other functions. But, you may define x in another function and
use x in the same way in that other function. Note all Dim statements should be specified
before any executable code.
Sometimes you want do define constants rather than variables. For example you might want
to specify a constant for gravity, and you write:
Const gravity As Single = 9.81
A constant statement could be specified either in the declarations part of the module (top of
module), or the declaration part of the function (i.e. before any executable code)
Passing arguments to a function or a procedure is accomplished by the statements in the
header of the function. When you define the function, you also define the variable types to be
passed, whereas when you call the function you only pass the variables, or values, e.g.
Function MySum(x As Single, y As Single)
MySum = x + y
End Function
Figure 9 Specification of arguments
You might then later from another function call MySum, e.g. x = MySum(3, 4). Note
that if you define an argument as e.g. Single, you cannot call the function with a variable of
e.g. Integer type. See the reference manual for variable types to use within VBA.
Loops are programming constructions that you will need. The simples loops are accomplished
either by the For statement, or the Do statement. In the following function two loop
constructions are used to count the numbers from 1 to 10:
Function Sum1To10()
Dim x As Integer
Dim s As Single
s = 0
For x = 1 To 10
s = s + x
Next x
Debug.Print s
s = 0
x = 0
Do While x < 10
x = x + 1
s = s + x
Loop
Debug.Print s
End Function
Figure 10 Loop constructions
In the first construction we use the For statement to specify the start, end, and optional the
increment of the counter variable x. Here we might have specified
For x = 2 To 10 Step 2
If we wanted to count only even numbers. The statements to be executed for each step are
specified before the Next statement.
In the Do While construction we instruct the computer to repeat as long a logical expression
is true. The statements to be executed for each step are specified before the Loop statement.
You might jump out of the loop by an Exit For, or Exit Do statement within the loop
construction.
Note that we want a function to return a value, this is done by assigning an expression to the
function name at the end of the function, e.g.
Sum1To10 = s
If a function should not return a value, you could alternatively use a procedure construction,
see the Excel reference for further information.
4.2Simple functions
In the previous example we calculated the probability of failure on demand (PFD) for the
safety valve by a number of steps. A more elegant approach would be to crate a function
accomplishing these calculations. In Figure 11 we have shown the VBA code for the PFDb
function, where “b” indicate that the beta-factor model is assumed. VBA (Visual Basic for
Applications) is the MS Office programming language.
Function PFD(lambda As Single, tau As Single, beta As Single, _
k As Integer, n As Integer)
' Beta factor model
' PFD = Probability of failure of demand
' PFD = Dependent part + Independent part
' Independent part = Combin(n,n-k+1)(lambda*(1-beta)*tau)^(n-k+1)/(n-k+2)
' lambda = total failure rate = lambda_commoncause + lambda_independent
'
PFD = lambda * tau * beta / 2 + _
((1 - beta) * lambda * tau) ^ (n - k + 1) / (n - k + 2) * _
Application.WorksheetFunction.Combin(n, n - k + 1)
End Function
Figure 11 VBA code for the PFD function
To invoke the VBA editor, just press <Alt>F11. In the VBA editor, choose Insert and Module
to create a module for storing the function.
From the Excel worksheet you might now call the function you have crated, e.g. in cell B17
you could specify =PFD(lambda,tau,beta,k,n).
When you crate functions in VBA you might want to get data stored in cells without passing
these values as arguments to the function. To accomplish this, use the Range() function in
VBA: The Range() function is specified as e.g. Range(“lambda”), where lambda is a cell
name.
4.3Advanced VBA functions
Sometimes you might want to create more complicated functions, e.g. a function for
numerical integration. Such a function would require the following elements:
 The name of the function to integrate
 Parameters used in this function
 Limits for the integration
The VBA language is not optimal for such programming because we could not pass a function
name as an argument to a function as we could do in e.g. FORTRAN or C++. A work around
approach would be to create a general purpose “Exec-function”, which takes two arguments,
an integer representing the function name (or number), and the argument, e.g.
Function execFunc(f As Integer, x As Single)
Select Case f
Case 1
execFunc = Sin(x)
Case 2
execFunc = Cos(x)
End Select
End Function
Figure 12 Simple Exec-function
If we in a program system need first to integrate the sin function, then the cos function we
could write a general purpose numerical integration function, which we first call with
argument 1, and the 2. To make the code more readable, we typically define constant like:
Public Const eFuncSin = 1, and so on. In the example above, we did not pass any
parameters to the execFunc. In some situations we would like to pas an argument, for example
we would like to have a more general cos function like a*Cos(b*x+c). One way to
accomplish this would be to store a, b and c in a variant variable. For example before calling
the numInt function we specify PassPar=ARRAY(1,2,3) to pas the parameters a=1, b=2
and c=3. We could then call the NumInt function by
NumInt(eFuncCos,PassPar,0,3.141).
It would then be the task of the NumInt procedure to pass further the variant PassPar to the
execFunc.
Another simpler way to pass arguments would be to create Public variables which cold be
accessed from any module.
4.4Built in functions
In VBA you could call a set of standard build in functions like sin(), cos(), log(), exp() etc.
These functions are available in all VBA settings (Word, Excel, Access etc). One strength of
Excel is that a number of Worksheet functions are also available from the VBA code. For
example the Normdist() function. However, to use these worksheet functions their name has
to be preceded by Application.WorksheetFunction.<FuncName>. For example
we might find the probability that a normally distributed variable is less than 2, when the
mean and standard deviation is 0 and 1 respectively by:
p = Application.WorksheetFunction.NormDist(2, 0, 1, True)
Note that from VBA the worksheet functions always are specified by their English name,
whereas from the worksheet you need to specify them by their national language (i.e.
depending on you Excel installation).
4.5Importing and exporting modules
Modules with VBA code are specific for each Excel file (workbook). If you create a module
in one Excel file it will not be available in another Excel file. There are two ways you may
copy VBA code from one file to another. The easiest way is to use the Clipboard to copy code
from one Excel file and paste into another Excel file. A more structured way is to establish
libraries of modules. To Export a module from Excel do the following:
1. Open the VBA editor by pressing <Alt F11>
2. Right click the module you will export, see Figure 13
3. Click Export File…, and select a folder to keep VBA modules
VBA modules are saved with the extension .bas and may be opened with a text editor. From
another Excel file the VBA code may be imported:
1. Open the VBA editor by pressing <Alt F11>
2. Right click modules,
3. Click Import File…, and select a file from the folder keeping VBA modules
Figure 13 Module library
5.VBA Examples
5.1The effective failure rate in age related models
In age based maintenance models an approximation for the effective failure rate could be
specified in Excel by:
lambdaE = EXP(GAMMALN(1+1/alpha))/MTTF)^alpha*tau^(alpha-1)
where tau, alpha and MTTF are variables defined in cells with corresponding names. This
function is often required in maintenance optimization problems, and it would be more
convenient to specify a VBA function, and then call this function each time we need to find
the effective failure rate:
Function LambdaEWApproxSimple(Tau As Single, Alpha As Single, MTTF As
Single)
If Alpha > 1 Then
LambdaEWApproxSimple = Gamma(1# / Alpha + 1#) ^ Alpha * _
Tau ^ (Alpha - 1#) / MTTF ^ Alpha
Else
LambdaEWApproxSimple = 1 / MTTF
End If
End Function
Figure 14 First approximation of the effective failure rate
Note that this function makes a call to the Gamma-function which could be implemented by:
Function Gamma(x As Single)
Gamma = Exp(Application.WorksheetFunction.GammaLn(x))
End Function
Figure 15 The Gamma() function
From the spread sheet in Excel, we may now call the LambdaEWApproxSimple()
function with the arguments tau, alpha and MTTF.
This approximation function is not very accurate when tau is higher than 10% of the MTTF.
A better approximation may be achieved by implementing a correction term.
Function LambdaEW(Tau As Single, Alpha As Single, _
MTTF As Single)
Dim lambda As Single
If MTTF > 0 Then
If Tau < 0.1 * MTTF Then
LambdaEW = LambdaEWApproxSimple(Tau, Alpha, MTTF)
Else
LambdaEW = LambdaEWApproxSimple(Tau, Alpha, MTTF) * _
(1# - 0.1 * Alpha * (Tau / MTTF) ^ 2 + _
(0.09 * Alpha - 0.2) * (Tau / MTTF))
End If
Else
LambdaEW = 1E+30
End If
End Function
Figure 16 A better approximation to the effective failure rate
Where the correction term ensures reasonable precision whenever tau < ½ MTTF. An even
better implementation would be to use an iterative procedure to find the renewal function
whenever when tau > ½ MTTF.
6.Monte Carlo Simulation
Monte Carlo simulation is a technique to do probability calculus when it is not straight
forward to use analytical techniques. The basic idea is that rather than working with the
distribution functions, or probability density function of random variables, we work with
these variables directly in either the work sheet, or the VBA code. To assign a (random) value
to a such variable we use the RAND() function from the worksheet, or the rnd() function from
the VBA modules. These two functions return a uniformly distributed variable in the interval
from 0 to 1. In the worksheet, we might then define a cell with name Duration, and specify
=RAND() as the formula for that cell. Excel will then generate a random number. To generate
a new number in the cell we ask Excel to do this by pressing the F9 key. If we want to see e.g.
the average duration, we could press F9 1000 times and write down the output, and then take
the average, of we could press F9 another 1000 times and count the number of times when the
Duration cell exceeds 0.9 to find Pr(Duration > 0.9) and so on.
It is, however, rather tedious to do this manually. We could write a VBA code that update the
field e.g. 1000 times, and for each time records the number, and then finally take the average
of the values that have been generated.
Note that the RAND() function generates a uniformly distributed variable. If you want
variables from other distributions you could write your own code.
7.Feedback
Feedback to this document could be emailed to jorn.vatn@ntnu.no
8.Index
arguments, 10
build in functions, 13
cell name
create from selection, 5
delete, 4
specification, 4
Const, 10
Dim, 10, 11
Do statement, 10
Do While, 11
For statement, 10
Loops, 10
name box, 4
Name Box, 4
plotting, 5
Private, 9
Public, 9
RAND(), 17
Range() function, 12
rnd(), 17
Solver, 6
variable name, 4
VBA, 9, 10, 11, 12, 13, 17
editor, 9
importing and exporting modules, 13
what if analysis, 8
worksheet functions, 13